These literally mean "early spring". The new year in Japan used to
be the same as the current Chinese new year, hence it was later than
now.

shoshun

初春

shōshun

頌春

The Japanese post office promises to deliver the cards on the morning
of the first of January if the card is posted within certain deadlines
in December.

If there has been a sad event such as a death in the family, that
person does not send any New Year's greeting cards that year, but
instead posts an apology letter, usually printed in black on
white. This is called mochuuketsurei (喪中欠礼). Many consider
that it is also not appropriate to send a New Year's card to a person
who has suffered a death in their family.